d-wave superconductors near surfaces and interfaces: A scattering matrix approach within the quasiclassical technique

A recently developed method [A. Shelankov and M. Ozana, Phys. Rev. B 61, 7077 (2000)] is applied to investigate d-wave superconductors in the vicinity of (rough) surfaces. While this method allows the incorporation of arbitrary interfaces into the quasiclassical technique, we discuss, as examples, diffusive surfaces and boundaries with small tilted mirrors (facets). The properties of the surface enter via the scattering matrix in the boundary condition for the quasiclassical Green's function. The diffusive surface is described by an ensemble of random scattering matrices. We find that the fluctuations of the density of states around the average are small; the zero bias conductance peak broadens with increasing disorder. The faceted surface is described in the model where the scattering matrix couples m in- and m out-trajectories $(mg~2).$ No zero bias conductance peak is found for [100] surfaces; the relation to the model of Fogelstr\"om et al. [Phys. Rev. Lett. 79, 281 (1997)] is discussed.